What Is The Final Step In Solving The Inequality $-2(5 - 4x) \ \textless \ 6x - 4$?A. $x \ \textless \ -3$ B. $x \ \textgreater \ -3$ C. $x \ \textless \ 3$ D. $x \ \textgreater \ 3$

by ADMIN 198 views

Introduction to Solving Inequalities

Solving inequalities is a crucial aspect of algebra, and it requires a deep understanding of the properties of inequalities. In this article, we will focus on solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 and determine the final step in solving this inequality.

Understanding the Given Inequality

The given inequality is −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4. To solve this inequality, we need to follow the order of operations (PEMDAS) and simplify the expression.

Step 1: Simplify the Left-Hand Side of the Inequality

The left-hand side of the inequality is −2(5−4x)-2(5 - 4x). To simplify this expression, we need to distribute the negative 2 to the terms inside the parentheses.

-2(5 - 4x) = -10 + 8x

Step 2: Rewrite the Inequality with the Simplified Left-Hand Side

Now that we have simplified the left-hand side of the inequality, we can rewrite the inequality as follows:

-10 + 8x \  \textless \  6x - 4

Step 3: Add 10 to Both Sides of the Inequality

To isolate the variable x, we need to add 10 to both sides of the inequality.

8x \  \textless \  6x - 4 + 10

Step 4: Simplify the Right-Hand Side of the Inequality

Now that we have added 10 to both sides of the inequality, we can simplify the right-hand side.

8x \  \textless \  6x + 6

Step 5: Subtract 6x from Both Sides of the Inequality

To further isolate the variable x, we need to subtract 6x from both sides of the inequality.

2x \  \textless \  6

Step 6: Divide Both Sides of the Inequality by 2

Finally, we can divide both sides of the inequality by 2 to solve for x.

x \  \textless \  3

Conclusion

In conclusion, the final step in solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 is to divide both sides of the inequality by 2, resulting in the solution x \textless 3x \ \textless \ 3. This solution indicates that the value of x is less than 3.

Final Answer

The final answer is x \textless 3x \ \textless \ 3.

Introduction to FAQs

In the previous article, we solved the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 and determined the final step in solving this inequality. In this article, we will address some frequently asked questions (FAQs) about solving this inequality.

Q: What is the first step in solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4?

A: The first step in solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 is to simplify the left-hand side of the inequality by distributing the negative 2 to the terms inside the parentheses.

Q: How do I simplify the left-hand side of the inequality?

A: To simplify the left-hand side of the inequality, you need to distribute the negative 2 to the terms inside the parentheses. This can be done by multiplying the negative 2 to each term inside the parentheses.

Q: What is the difference between the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 and the inequality −2(5−4x) \textgreater 6x−4-2(5 - 4x) \ \textgreater \ 6x - 4?

A: The inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 is a less than inequality, while the inequality −2(5−4x) \textgreater 6x−4-2(5 - 4x) \ \textgreater \ 6x - 4 is a greater than inequality. This means that the solution to the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 will be different from the solution to the inequality −2(5−4x) \textgreater 6x−4-2(5 - 4x) \ \textgreater \ 6x - 4.

Q: How do I know which direction to go when solving an inequality?

A: When solving an inequality, you need to determine the direction of the inequality. If the inequality is a less than inequality, you will go in the opposite direction of the inequality. If the inequality is a greater than inequality, you will go in the same direction as the inequality.

Q: What is the final step in solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4?

A: The final step in solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 is to divide both sides of the inequality by 2, resulting in the solution x \textless 3x \ \textless \ 3.

Q: What does the solution x \textless 3x \ \textless \ 3 mean?

A: The solution x \textless 3x \ \textless \ 3 means that the value of x is less than 3. This means that any value of x that is less than 3 will satisfy the inequality.

Q: How do I graph the solution x \textless 3x \ \textless \ 3 on a number line?

A: To graph the solution x \textless 3x \ \textless \ 3 on a number line, you need to draw a line at x = 3 and shade the region to the left of the line. This represents all the values of x that are less than 3.

Conclusion

In conclusion, solving the inequality −2(5−4x) \textless 6x−4-2(5 - 4x) \ \textless \ 6x - 4 requires a deep understanding of the properties of inequalities. By following the steps outlined in this article, you can solve this inequality and determine the final step in solving this inequality. Additionally, this article addresses some frequently asked questions (FAQs) about solving this inequality, providing a comprehensive understanding of the solution.

Final Answer

The final answer is x \textless 3x \ \textless \ 3.